WASHINGTON — Mitt Romney sought on Tuesday to quell the controversy surrounding his comments disparaging nearly half of the electorate, attempting to engage in a philosophical debate over the role of government even as some in his party began distancing themselves from their presidential standard-bearer.

As the full 49-minute video from a private May fund-raiser emerged online, Romney largely stuck with his controversial comment that President Obama’s supporters are “dependent on government,” even as he acknowledged that some among his targeted 47 percent cannot be so easily categorized.

In newly released portions of the video, made without Romney’s knowledge at the Florida fund-raising event, he was also seen telling the donors that the Israeli-Palestinian conflict “is going to remain an unsolved problem” in large part because “the Palestinians have no interest whatsoever in establishing peace.”

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“I look at the Palestinians not wanting to see peace anyway, for political purposes — committed to the destruction and elimination of Israel, and these thorny issues — and I say, ‘There’s just no way.’ ”

In one striking passage that some saw as indicating a Romney White House would not actively pursue an Israeli-Palestinian peace agreement, he said: “We kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it.” A spokeswoman for Romney’s campaign said Tuesday that as president he would still address the conflict and attempt to reach a two-state solution.

Romney’s remark triggered rebukes from Palestinian leaders, and the video overall continued to reverberate across the political world.

With polls showing that Obama is continuing to extend his lead in the polls just 48 days before the election, Romney’s campaign held a conference call with top donors on Tuesday to reassure them that the situation was under control and that the campaign was marching forward.

Obama, in his first public comments on the matter, took aim at Romney’s stated plan to disregard the 47 percent Romney deemed lacking in “personal responsibility.”

Appearing on David Letterman’s show, Obama said that anyone who wants to be president has to “work for everyone, not just for some.”

“There are not a lot of people out there who think they are victims,” he said, contradicting his Republican rival’s remark in the video that almost half of all Americans think of themselves as victims and expect government support.

Specifically, Romney said in the video that 47 percent of the electorate don’t pay federal income taxes and are “dependent upon government — victims” who believe “that they are entitled to health care, to food, to housing, to you-name-it.” He added: “My job is not to worry about those people.”

The challenge for Romney is that the 47 percent figure includes a wide swath of voters, including some 16 million seniors who do not owe federal income taxes due to tax breaks for which they are eligible.

Others receive credits to help offset child care costs, taking their taxable income below cutoff levels, or because they serve in the military.

In his first interview since the clip emerged, Romney attempted to stand by the underlying philosophy of his statement — that government should have a lesser role in people’s lives — even while he tried to say that he was not writing off the 47 percent who don’t pay taxes, as he indicated he was in the video.

“There are a number of retirees, members of the military and so forth who aren’t paying taxes, and that’s as it should be,” Romney told Fox News’s Neil Cavuto on Tuesday afternoon. “But I do believe that we should have enough jobs and enough take-home pay such that people have the privilege of higher incomes that allow them to be paying taxes. I think people would like to be paying taxes.”

Republicans were divided over Romney’s comments, with some saying he was deeply misinformed and had found a way to alienate much of the electorate by characterizing all those who don’t pay income taxes as victims who could not be convinced to take personal responsibility for their lives.

US Senator Scott Brown — who shares top political strategists with Romney — quickly distanced himself from his fellow Massachusetts Republican.

“That’s not the way I view the world,” Brown said in a statement. “As someone who grew up in tough circumstances, I know that being on public assistance is not a spot that anyone wants to be in.”

Bill Kristol, editor of the Weekly Standard, called Romney’s comments “stupid and arrogant” and suggested that Romney step down and allow Republicans to instead have a ticket that would include Paul Ryan and Marco Rubio.

But some conservative Republicans, who have been eager for a fight over government entitlement programs, saw in the fund-raiser video a more confident and plainspoken Romney they want to see more of.

“This could be the opportunity for Romney, and for that campaign, to finally take the gloves off and take the fear off and just start explaining conservatism, start explaining liberty to people and what it means.” Rush Limbaugh said Tuesday on his widely syndicated radio show.

The identity of the person who taped Romney’s blunt comments at the fund-raiser remained a mystery Tuesday.

James Carter IV, the grandson of Jimmy Carter, the former president, said he played a key role in helping to release the video, contacting a source who had been posting short clips online in recent weeks and persuading the source to provide the video to Mother Jones, a liberal magazine.

Carter did not identify the video source, saying only that it was safe to assume it was not one of Romney’s donors.

He told NBC News that he was motivated to help make the video public in part because of Romney’s frequent criticism of his grandfather.

He said he e-mailed his grandfather the story about the tape and got a response early Tuesday morning: “James: This is extraordinary. Congratulations! Papa.”

Romney several times on Tuesday referenced a 1998 video clip that surfaced just before his Fox interview, which shows Obama, then an Illinois state senator, advocating for helping the poor through “redistribution.”

“The trick is figuring out how do we structure government systems that pool resources and hence facilitate some redistribution,” Obama says in the clip, to which the conservative website the Drudge Report posted a link. “Because I actually believe in redistribution — at least at a certain level to make sure that everybody’s got a shot.”

“I know some believe that government should take from some to give to the others,” Romney said in the Fox interview. “I think that’s an entirely foreign concept.”

Over the course of Tuesday, new portions of the secret video surfaced, showing that Romney covered a range of issues as he courted the wealthy donors at the Boca Raton home of investor Marc Leder.

Romney went through several reasons why a Palestinian state would not work — largely because of its close proximity to Israel, he said, and because Iran would try to exert influence.

In July, he told the Israeli newspaper Haaretz, “I believe in a two-state solution which suggests there will be two states, including a Jewish state.”

Romney also highlighted the need to prevent Iran from obtaining a nuclear weapon, but he did it in a different way from what he does on the campaign trail.

“If I were Iran — a crazed fanatic — I’d say let’s get a little fissile material to Hezbollah, have them carry it to Chicago or some other place,” he said.

“I mean this is where we have — where America could be held up and blackmailed by Iran, by the mullahs, by crazy people,” he added. “So we really don’t have any option but to keep Iran from having a nuclear weapon.”